Table 1. The set of candidate models.

MODEL	Linear Predictor
m1	s(kW:Period) + s(Depth: Period) + Period + Country+ s(Fisherman, bs = “re”)
m2	s(kW: Period) + s(Depth: Period) +Period + Country + GSA +s(Fisherman, bs = “re”)
m3	s(kW: Period) + s(Depth) + Period + Country + GSA + s(Fisherman, bs = “re”)
m4	s(kW) + s(Depth) + Period + Country + GSA +s(Fisherman, bs = “re”)
m5	s(kW: Period) + Depth + Period+ Country + GSA +s(Fisherman, bs = “re”)
m6	s(kW: Period) + Depth + Period+ Country + s(Fisherman, bs = “re”)
m7	s(kW: Period) + Depth + Period+ GSA + s(Fisherman, bs = “re”)
m8	s(kW: Period) +Period+ Country + s(Fisherman, bs = “re”)
m9	s(kW: Period) + Country + s(Fisherman, bs = “re”)

GSA = Geographical Sub-Areas

s() is a smooth function represented using penalized regression splines [25].

Covariate “Fisherman” was estimated through penalized random effects (bs = “re”).